One day they will accept. It's just a matter of time now. The first steps towards adoption they have already done. For an example, banks in my country offer Bitcoin as investment alternative, although you can't access your Bitcoins directly, without using the bank. However, it doesn't have to be like this forever. Soon I believe they will become less strict, allowing customers to deposit and cashout their BTCs to external addresses, although some kind of KYC must be implied along the process.
The question is: Will regulators allow it? The US is a pro-crypto country, so it wouldn't have a problem with this. But what about other countries such as those within the EU bloc and BRICS? I'm pretty sure they won't allow banks to offer crypto services to their customers. Besides, Bitcoin is NOT legal tender. So banks would be "playing" at their own risk.
Why care about banks, though? Isn't Bitcoin good on its own? With Bitcoin, you can truly be your own bank. I guess the OP doesn't understand what Bitcoin is all about. It's more than just money or "digital gold". It's a movement, a revolution meant to bring back monetary freedom to the people. I hope it fulfills its purpose, before it's too late.